A residually finite group is a group 
for which each nonidentity element has a nonidentity image
under a group homomorphism to some finite
group. Equivalently, the intersection of the
kernels of all such homomorphisms
is trivial. Denote that intersection by 
. For example, 
is residually finite because reduction
modulo a suitable positive integer separates
any nonzero integer from
zero.
Residually Finite Group
See also
Finite Group, Group Homomorphism, Hyperbolic Group, Normal SubgroupExplore with Wolfram|Alpha
References
Löh, C. Geometric Group Theory: An Introduction. Cham, Switzerland: Springer, 2017. https://doi.org/10.1007/978-3-319-72254-2.Cite this as:
Weisstein, Eric W. "Residually Finite Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ResiduallyFiniteGroup.html